{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/knowledge-graph-completion-via-complex-tensor","title":"Knowledge Graph Completion via Complex Tensor Factorization","arxiv_id":"1702.06879","date":"2017-02-22","proceeding":null,"authors":["Théo Trouillon","Christopher R. Dance","Johannes Welbl","Sebastian Riedel","Éric Gaussier","Guillaume Bouchard"],"abstract":"In statistical relational learning, knowledge graph completion deals with\nautomatically understanding the structure of large knowledge graphs---labeled\ndirected graphs---and predicting missing relationships---labeled edges.\nState-of-the-art embedding models propose different trade-offs between modeling\nexpressiveness, and time and space complexity. We reconcile both expressiveness\nand complexity through the use of complex-valued embeddings and explore the\nlink between such complex-valued embeddings and unitary diagonalization. We\ncorroborate our approach theoretically and show that all real square\nmatrices---thus all possible relation/adjacency matrices---are the real part of\nsome unitarily diagonalizable matrix. This results opens the door to a lot of\nother applications of square matrices factorization. Our approach based on\ncomplex embeddings is arguably simple, as it only involves a Hermitian dot\nproduct, the complex counterpart of the standard dot product between real\nvectors, whereas other methods resort to more and more complicated composition\nfunctions to increase their expressiveness. The proposed complex embeddings are\nscalable to large data sets as it remains linear in both space and time, while\nconsistently outperforming alternative approaches on standard link prediction\nbenchmarks.","url_abs":"http://arxiv.org/abs/1702.06879v2","url_pdf":"http://arxiv.org/pdf/1702.06879v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"knowledge-graph-completion-via-complex-tensor","repo_url":"https://github.com/ttrouill/complex","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":{"status":"ok","spdx":"NOASSERTION"}},{"paper_slug":"knowledge-graph-completion-via-complex-tensor","repo_url":"https://github.com/Accenture/AmpliGraph","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"tf","reach":{"status":"ok","spdx":"Apache-2.0"}}],"tasks":[{"task_slug":"knowledge-graph-completion","task_name":"Knowledge Graph Completion"},{"task_slug":"knowledge-graphs","task_name":"Knowledge Graphs"},{"task_slug":"link-prediction","task_name":"Link Prediction"},{"task_slug":"relational-reasoning","task_name":"Relational Reasoning"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[{"leaderboard":"/sota/knowledge-graphs-on-fb15k","task":"Knowledge Graphs","dataset":"FB15k","model":"COMPLEX","rank_in_archive_order":2,"of":2,"metrics":{"MRR":"0.587"},"uses_additional_data":false},{"leaderboard":"/sota/link-prediction-on-fb15k","task":"Link Prediction","dataset":"FB15k","model":"Complex","rank_in_archive_order":18,"of":23,"metrics":{"Hits@1":"0.599","Hits@10":"0.840","Hits@3":"0.759","MRR":"0.692"},"uses_additional_data":false}],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1702.06879","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}